Koichi Tohei Sensei teaches that the movements of the jo that we do are a combination of movements adopted from yari, naginata, and staff.

This is my opinion too. Moreover, regardless of the origin of the Jo, whether it started as a Yari or Naginata, the fact that it can be used on both ends, to do both striking and poking techniques, this all gives the Jo a flexibility and an advantage over both weapons. (Naginata was a women's weapon by the way).